having trouble factoring

Question

15y2+14y-16

Answer 1

You can use the quadratic formula to solve 15y² + 14y + 6 = 0

You will find that y = 2/3 or y = -8/5

 

There is a formula you can use to factor polynomials, when x₁ and x₂ are solutions:

                                        ax²+bx+c = a(x−x₁)(x−x₂)

 

In your problem you are using the variable y, but you can substitute 2/3 for x₁ and -8/5 for x₂.

 

Notice that this would become 15y² - 14y - 16 = 15(y -2/3)(y + 8/5)

 

Notice that the denominators of 2/3 and 8/5 are 3 and 5, and that 3 * 5 = 15, you can use this to help get rid of the fractions by re-arranging this to be 3*5(y -2/3)(y + 8/5),

3(y - 2/3)* 5(y - 8/5)  this will give you whole numbers: (3y -2)(5y -8)